SOLUTION: Help please!! Add the fractions {{{q/q^2+5q+6}}} and {{{1/q^2 +3q+2}}}

Question 40067: Help please!!
Add the fractions and
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Well from
q/(q^2 + 5q + 6) + 1/(q^2 + 3q +2)
we factor the denominators and then look for the lowest common denominator to change each fraction into. Once we do that we can combine the fractions. Hopefuly something will simplify. So here goes...
q/(q^2 + 5q + 6) + 1/(q^2 + 3q +2) =
q/(q+2)(q+3) + 1/(q+2)(q+1) =
q(q+1)/(q+1)(q+2)(q+3) + (q+3)/(q+1)(q+2)(q+3) =
(q^2+q)/(q+1)(q+2)(q+3) + (q+3)/(q+1)(q+2)(q+3) =
(q^2+2q+3)/(q+1)(q+2)(q+3)
Nothing else simplifies...we are done...
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